Predicting predator-prey populations

Desired results

Here’s an approximation of reality: The hare birth rate is constant, as their food supply is unlimited. Hares only die when eaten by a lynx, and the number of hares eaten is proportional to how often hares & lynxes meet, i.e., the chance of a lynx catching a hare. The lynx birth rate is also proportional to how often hares & lynxes meet, i.e., the food available for each lynx family. Lynxes only die from natural causes, and their death rate is constant. Lotka & Volterra, 1926 Dr. SiemannDr. Siemann, EEB

Computational Thinking Recipe (Algorithm) Relevant input Answer Abstraction Automation Problem description Computational goal Information extraction Algorithm design Algorithm implementation

Hares’ & Lynxes’ Populations Recipe (Algorithm) ??? Problem description Computational goal Information extraction Algorithm design Algorithm implementation

Algorithm Design – Decomposition 1.Generate population data. Repeatedly, a.Generate next populations of predator & prey. 2.Display population data.

Algorithm Design – Refinement 1.Store original populations. 2.Generate population data. Repeatedly, a.Generate next populations of predator & prey. b.Store new populations. 3.Display stored population data.

Lotka & Volterra, 1926 The hare birth rate is constant, as their food supply is unlimited. Hares only die when eaten by a lynx, and the number of hares eaten is proportional to how often hares & lynxes meet, i.e., the chance of a lynx catching a hare. The lynx birth rate is also proportional to how often hares & lynxes meet, i.e., the food available for each lynx family. Lynxes only die from natural causes, and their death rate is constant. Hare annual pop. change Lynx annual pop. change

Initially (Year 0) Year 1Year 2Year 3 # Hares 100 Hares born 4040 Hares eaten 15 #Lynxes Lynxes die 10 Lynxes born Hare annual pop. changeLynx annual pop. change Rounding all #s.

Algorithm Design – Refinement

Suggested Readings Predator-prey models Lotka-Volterra equation Wolves & Moose of Isle Royale – Esp. the Data sectionData – A technical paper about population cyclestechnical paper